3. A treed that never gave up on its dream to flourish. [10 points] Let T be a spanning tre

n edge cost function c. T is defined to have the cycle property if for any edge

the cycle generated by adding e' to T. Also, T is defined to have the cut property if for any edge

for all e' in the cut defined by e. Show that the following three statements are equiva

 1. T has the cycle property.
 2. T has the cut property.
 3. T is a minimun cost spanning tree.